document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998671>Question 998671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1 , 8 , 18 ... <BR>\n" );
document.write( "in the sequence above , the first term is 1 and the sum of the first n terms is equal to 3 to the power n for all n > 1 <BR>\n" );
document.write( "what is the fourth term in the sequence ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616429 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=616429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=1 ALIGN=MIDDLE  ALT=\"a%5B1%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=8 ALIGN=MIDDLE  ALT=\"a%5B2%5D=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2Ba%5B2%5D=1%2B8=9=3%5E2 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Ba%5B2%5D=1%2B8=9=3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The sum of the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms, going all the way to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=18 ALIGN=MIDDLE  ALT=\"a%5B3%5D=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > , is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D=9%2Ba%5B3%5D=9%2B18=27=9%5E3 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D=9%2Ba%5B3%5D=9%2B18=27=9%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The sum of the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms, going all the way to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D ALIGN=MIDDLE  ALT=\"a%5B4%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the fourth term (to be found), is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D%2Ba%5B4%5D=27%2Ba%5B4%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D%2Ba%5B4%5D=27%2Ba%5B4%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4=81 ALIGN=MIDDLE  ALT=\"3%5E4=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2Ba%5B4%5D=81 ALIGN=MIDDLE  ALT=\"27%2Ba%5B4%5D=81\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=81-27 ALIGN=MIDDLE  ALT=\"a%5B4%5D=81-27\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=highlight%2854%29 ALIGN=MIDDLE  ALT=\"a%5B4%5D=highlight%2854%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "EXTRA:<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2Ba%5B2%5D%2B%22...%22%2Ba%5Bn-1%5D%2Ba%5Bn%5D=3%5En ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Ba%5B2%5D%2B%22...%22%2Ba%5Bn-1%5D%2Ba%5Bn%5D=3%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2Ba%5B2%5D%2B%22...%22%2Ba%5Bn-1%5D=3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2Ba%5B2%5D%2B%22...%22%2Ba%5Bn-1%5D=3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=%28a%5B1%5D%2Ba%5B2%5D%2B%22...%22%2Ba%5Bn-1%5D%2Ba%5Bn%5D%29-%28a%5B1%5D%2Ba%5B2%5D%2B%22...%22%2Ba%5Bn-1%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=3%5En-3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=3%5En-3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=3%2A3%5E%28n-1%29-3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=3%2A3%5E%28n-1%29-3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=%283-1%29%2A3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=%283-1%29%2A3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=2%2A3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=2%2A3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "All of that for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3E1 ALIGN=MIDDLE  ALT=\"n%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , of course, as the problem specified.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1 ALIGN=MIDDLE  ALT=\"n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the sum of the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1 ALIGN=MIDDLE  ALT=\"n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=1 ALIGN=MIDDLE  ALT=\"a%5B1%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which is not equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E1=3 ALIGN=MIDDLE  ALT=\"3%5E1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=2%2A3%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D=2%2A3%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is how I mentally calculated <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=2%2A3%5E3=2%2A27=54 ALIGN=MIDDLE  ALT=\"a%5B4%5D=2%2A3%5E3=2%2A27=54\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81-54 ALIGN=MIDDLE  ALT=\"81-54\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the type of calculation that I have hated to do since the first grade. </SPAN>\n" );
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